# Why model-theorists shouldn’t think that ACF is easy

## Hans Schoutens

### The City University of New York

We all learned that stability theory derived many of its ideas from what happens in ACF, where everything is nice and easy. After all ACF has quantifier elimination and is strongly minimal, decidable, superstable, uncountably categorical, etc. However, my own struggles with ACF have humbled my opinion about it: it is an awfully rich theory that encodes way more than our current knowledge. I will discuss some examples showing how “difficult” ACF is: Grothendieck ring, isomorphism problem, set-theoretic intersection problem. Oddly enough, RCF seems to not have any of these problems. It is perhaps my ignorance, but I have come to think of RCF as much easier. Well, all, of course, is a matter of taste.

Professor Schoutens is a professor of mathematics at the City University of New York, and conducts research in algebraic model theory, commutative algebra, algebraic geometry, rigid analytic geometry and valuation theory.